Abstract
We present new algorithms for finding short cycles (of length at most 6) in planar graphs. Although there is an O(n) algorithm for finding any fixed subgraph H in a given n-vertex planar graph [5], the multiplication constant hidden in “O” notation (which depends on the size of H) is so high, that it rather cannot be used in practice even when |V(H)| = 4. Our approach gives faster “practical algorithms” which are additionally much easier to implement.
As a side-effect of our approach we show that the maximum number of k-cycles in n-vertex planar graph is \(\Theta (n^{\lfloor \frac{k}{2} \rfloor})\).
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Kowalik, Ł. (2003). Short Cycles in Planar Graphs. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_25
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DOI: https://doi.org/10.1007/978-3-540-39890-5_25
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